Measurement of the third order nonlinear susceptibility of paratellurite single crystal using multiplex CARS

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Measurement of the third order nonlinear susceptibility of paratellurite single crystal using multiplex CARS

Zakaniaina Rajaofara, Philippe Leproux, Erwan Capitaine, Hideaki Kano, Tomokatsu Hayakawa, Philippe Thomas, Jean-René Duclère, Vincent Couderc

To cite this version:

Zakaniaina Rajaofara, Philippe Leproux, Erwan Capitaine, Hideaki Kano, Tomokatsu Hayakawa, et al.. Measurement of the third order nonlinear susceptibility of paratellurite single crystal us- ing multiplex CARS. AIP Advances, American Institute of Physics- AIP Publishing LLC, 2019, 9,

�10.1063/1.5113478�. �hal-03095077�

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using multiplex CARS

Cite as: AIP Advances 9, 105301 (2019); https://doi.org/10.1063/1.5113478

Submitted: 04 June 2019 . Accepted: 27 September 2019 . Published Online: 03 October 2019 Zakaniaina Rajaofara, Philippe Leproux, Erwan Capitaine , Hideaki Kano, Tomokatsu Hayakawa , Philippe Thomas , Jean-René Duclère, and Vincent Couderc

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^ARTICLE scitation.org/journal/adv

Measurement of the third order nonlinear susceptibility of paratellurite single crystal using multiplex CARS

Cite as: AIP Advances9, 105301 (2019);doi: 10.1063/1.5113478 Submitted: 4 June 2019•Accepted: 27 September 2019• Published Online: 3 October 2019

Zakaniaina Rajaofara,^1,2 Philippe Leproux,² Erwan Capitaine,² Hideaki Kano,³ Tomokatsu Hayakawa,⁴ Philippe Thomas,¹ Jean-René Duclère,¹ and Vincent Couderc^2,a)

AFFILIATIONS

1Institut de Recherche sur les Céramiques, UMR 7315 CNRS-Université de Limoges, Centre Européen de la Céramique, 12, rue Atlantis, 87068 Limoges Cedex, France

2Institut XLIM, UMR 7252 CNRS – Université de Limoges, 123, Avenue Albert Thomas, 87060 Limoges Cedex, France

3Department of Applied Physics, Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

4Field of Advanced Ceramics, Department of Life Science and Applied Chemistry, Nagoya Institute of Technology, Gokiso, Showa, Nagoya 466-8555, Japan

a)Corresponding author:[email protected]

ABSTRACT

We report the extraction of the real part of the third order nonlinear susceptibility for a c-cut paratellurite (TeO2−α) single crystal using the nonresonant contribution of the multiplex coherent anti-Stokes Raman scattering (M-CARS) signal. Using fused silica and SF57 as nonlinear reference materials, we derive the absolute value of the real part of the electronic third order susceptibility and we evidence the in-plane modulation of the nonlinear refractive index. These results are in total agreement with those recently obtained by the z-scan method.

© 2019 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).https://doi.org/10.1063/1.5113478., s

I. INTRODUCTION

The coherent Raman anti-Stokes scattering (CARS) technique has been commonly used for microscopy applications thanks to its wide ability to probe the vibrational resonances of biological samples. The first measurement of CARS radiation has been obtained in 1965 by P. D. Maker and R. W. Terhune¹after the theoretical pre- diction published by J. A. Armstronget al.in 1962.²In its simplest configuration, CARS system is used to probe a single vibrational mode which is stimulated by the beating of two monochromatic syn- chronized waves called pump (ωp) and Stokes (ωs) waves. When the power density exciting the sample is sufficiently strong and the frequency difference between pump and Stokes waves matches that of a vibrational mode, a coherent response from the matter is observed. The nonlinear mechanism is driven by a four-wave mixing

process delivering an anti-Stokes wave (ωas) which satisfies the energy conservation law: ωp + ωp − ωs = ωas. More recently dual broadband CARS has been demonstrated allowing simultaneous identification of several vibrational modes.³ Later, Zumbusch et al.⁴ implemented CARS in a microscope for vibrational imaging of chemical and biological samples. Then multiplex CARS (M-CARS) has been introduced by using supercontinuum generated in microstructured optical fibers. CARS spectra covering more than 3500cm⁻¹have been obtained by this method on a large diver- sity of samples.^5,6Systematically, M-CARS vibrational signatures are accompanied by an additional nonlinear signal called nonresonant background (NRB), which is provided by the electronic response of the matter. The NRB is coherent with the vibrational signal and thus strongly modulates the total CARS intensity which is given by the Eq.1:⁷

AIP Advances9, 105301 (2019); doi: 10.1063/1.5113478 9, 105301-1

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( ) ∝ ∣ NR( )∣ ∣ R ( )∣ [ NR( )] [ R ( )]

(1) whereχ⁽³⁾_NR andχ⁽³⁾_R are the nonresonant and the resonant complex third order nonlinear susceptibilities respectively.

The χ⁽³⁾_NR term introduces a broadband response clearly visible on the entire M-CARS spectra. In most cases, vibrational signature is extracted from the spectra by using phase retrieval algo- rithms.^8,9 As well, experimental approaches have been developed to reduce or suppress the NRB in M-CARS configuration.^10,11On another side, in the case where no vibrational contribution arises and where the multi photon absorption is neglected, the CARS intensity is only feeded by the nonlinear electronic contribution with a direct relation with the square of the real part of the third order susceptibility (or Kerr susceptibility) as shown in Eq.2. Then measurement of Kerr response becomes possible with a M-CARS system.

ICARS(ω) ∝ [Re(χ_NR⁽³⁾(ω))]² (2) In this paper we present the extraction of the real part of the electronic responseRe[χ_NR⁽³⁾(ω)]of a c-cut TeO2−αsingle crystal by considering the NRB of M-CARS spectra. The absolute value of the nonlinear response is obtained by comparison with fused silica SiO2and Schott N-SF57 glasses used as standard nonlinear media with known nonlinear parameters. We show that the pure nonlinear electronic contribution can be obtained by a broadband spectral analysis excluding the vibrational region, where dispersion ofχ_R⁽³⁾ is observed.¹²The results are then compared with the recent data obtained by Duclèreet al.from z-scan experiments.¹³ Finally, we evaluate the in-plane modulation of the nonlinear refractive index of TeO2−α.

II. EXPERIMENTAL SETUP

The multiplex CARS setup is presented inFig. 1. The source is a Sirius Spark Laser which delivers 60 ps pulses at 1064 nm with 150 kHz repetition rate. The laser beam is split into two

FIG. 2. Broadband spectrum of the Stokes beam (a) at the output of the PCF and (b) after the excitation objective (Olympus UplanSAPo x60).

parts by using a half-wave plate and a Glan-Taylor polarizer. The first part is injected in a photonic crystal fiber (PCF) to gener- ate a supercontinuum spectrum between 600 nm and 1700 nm (seeFig. 2).

A long pass filter (Thorlabs, FEL1050) selects its infrared range between 1050 nm and 1700 nm to be used as the Stokes wave. The second part is used as pump wave which is sent in a delay line to compensate the propagation in the nonlinear microstructured optical fiber undergone by the broadband Stokes wave. The two incident beams are then recombined by means of a dichroic mirror (Sem- rock, NFD01-1064-25x36). Both Stokes and pump are randomly and linearly polarized respectively and are focused at the sample by a microscope objective (Obj 1: Olympus, UPlanSApo 60x, N.A.

= 1.2, water immersion). This water immersion objective is used to maximize the numerical aperture and to ensure a high spatial

FIG. 1. CARS experimental setup.λ/2, half-wave plate; GTP, Glan-Taylor polarizer; PCF, photonic crystal fiber.

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FIG. 3. TeO2−αcrystal sample orientation with respect to its crystallographic axes⃗a-TeO2,⃗b-TeO2and⃗c-TeO2(red arrows). The Stokes is randomly polarized (blue arrows) while the pump polarization is along y axis (black arrow).

resolution. Because of the nature of the crystal, no detrimental inter- action between the sample and the immersion fluid (Zeiss, Immersol W 2010) is observed and, the focus plane being in the crystal, no parasitic CARS signal from the immersion fluid is generated. The measured power of the pump behind the excitation objective is 16.1 mW±0.1 mW and that of Stokes is 5.8 mW±0.1 mW. The anti- Stokes beam is then collected by a second microscope objective (Obj 2: Nikon, S Plan Fluor ELWD 60x, N.A.=0.7) before being sent into the spectrum analyzer (CCD Horiba, Synapse) with a maximum resolution of 1cm⁻¹.

The sample is a c-cut paratellurite single crystal with a heli- cal structure and four-fold symmetry properties¹⁴ set on a man- ual rotation stage. As a consequence, data will be collected over a[0^○−360^○]range using a rotation step of 10^○. Then, they will be averaged and rescaled on a[0^○−90^○]range (90^○being strictly equivalent to 0^○by symmetry). Its two crystallographic axes labeled

⃗

a-TeO2and ⃗b-TeO2are referenced in the rotating mount at 90^○ and 0^○ respectively (seeFig. 3). The initial polarization direction of the pump beam is oriented at 45^○along the bisector of⃗a-TeO2

and⃗b-TeO2.

III. RESULTS AND DISCUSSION A. Extraction ofRe[χ⁽³⁾_NR]

The broadband traces of TeO2− αCARS spectra for different rotation stage angles are given inFig. 4where the anti-Stokes intensity is plotted versus the wavenumber. In this figure, a single vibrational signature of TeO2−αis recorded at 644cm⁻¹and is assigned to the stretching modes of the equatorial Te-O bonds in TeO4trigonal bipyramid units.¹⁵In all the remaining frequency range, only the NRB is still visible. It is also important to under- line that in our case, the vibrational signature of the TeO2 − α crystal is significantly high compared to the NRB signal. In these conditions, and to avoid any parasitic effect of the vibrational signature, the NRB signature used to extract theRe[χ⁽³⁾_NR]is exploited only for wavenumbers beyond 1000cm⁻¹. The output signal level is then quadratically dependent on the pump inensity and linearly dependent on the Stokes intensity at each wavelength according to Eq.3.

ICARS(ω) ∝ [Re(χ_NR⁽³⁾)]²Ip(ω)²Is(ω) (3)

The raw anti-Stokes wave intensity obtained at the sample output is, thus, divided by the Stokes wave spectral profile (see Fig. 4) to get rid of the initial supercontinuum variation. The normalized experimental data show, at first glance, that the anti- Stokes intensity seems to be roughly constant between 1000cm⁻¹ and 3000 cm⁻¹. In fact, a carefull observation clearly reveals that there is a moderate evolution of the NRB with respect to the crystal in-plane orientation (See further discussion in Sec.III B).

In order to extract a quantitative mean value of the nonlinear susceptibility of the paratellurite crystal, we first averaged all the curves obtained for different rotation stage angles and compared them with those obtained for fused silica and SF57 samples. The comparison is presented on Fig. 5 in log scale.

FIG. 4. CARS spectra of TeO2−αnormalized by the Stokes broadband spectrum for different rotation stage angles. Inset: Example of raw CARS spectrum of TeO₂

−αfor a given position of the rotation stage.

AIP Advances9, 105301 (2019); doi: 10.1063/1.5113478 9, 105301-3

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FIG. 5. Comparison of the square root of CARS NRB level of fused silica (red curve), SF57 (green curve) and TeO₂ − α (blue curve) in log scale (a). Zoomed-in CARS spectra of SF57 (b) and SiO₂ (c). Black dashed lines delimitate the spectral range of the NRB between 1000cm⁻¹and 3000cm⁻¹that was used to extract the meann2value.

TABLE I. Comparison of the ratio^Re[χ

(3)(TeO2)]

Re[χ⁽³⁾(SiO2)] for different methods (Z-scan¹³/CARS/THG²²).

Z-scan CARS (this work) THG

λpump(nm) 800 1064 1900

Re[χ⁽³⁾(TeO₂)]

Re[χ⁽³⁾(SiO2)] 49.1 48.9 50.4

(TeO2−αcrystal) (TeO2−αcrystal) (pure TeO2glass)

As the nonlinear refractive indexn2is proportional to Re[χ_NR⁽³⁾] according to Eq.4¹⁶

n2=3Re[χ⁽³⁾_NR]

4n²₀ε0c (4)

wheren0is the linear refractive index,cis the light velocity andε0

the vacuum permittivity, we deduced the value ofn2of TeO2−α.

All our results and comparisons to the relevant literature values are summarized inTable IandTable II.

TABLE II. Values of nonlinear refractive indexn2of TeO2−α, fused silica and SF57.

Sample λpump(nm) n2(m².W⁻¹)

SiO217 1053 0.274±0, 17×10⁻¹⁹

SF57^18–21 1064 2.25×10⁻¹⁹

TeO2−α¹³(by Z-scan) 800 5.86×10⁻¹⁹ TeO2−α(this work) 1064 5.72±0.73×10⁻¹⁹ SF57 (this work) 1064 2.27±0.14×10⁻¹⁹

In our configuration, the square root of the mean NRB level of TeO2−α is 48.9 and 3.8 times higher than those of fused silica and SF57 respectively. In these conditions, the meann2value of TeO2−αis estimated to be 5.72±0.73×10⁻¹⁹m²W⁻¹at 1064 nm assuming then2 value of silica close to 0.274×10⁻¹⁹m² W⁻¹ at 1053 nm.¹⁷ Then we can compare this value to the one recently reported by Duclèreet al.¹³which is 5.86×10⁻¹⁹m²W⁻¹(measurement realised at 800 nm by using z-scan technique in femtosecond domain for the exact same TeO2−αcrystal). Excellent agreement is observed between both values. Finally, by using the same approach, the extracted value of SF57 is then 2.27±0.14×10⁻¹⁹m²W⁻¹, thus once again very close to the value of 2.25×10⁻¹⁹m²W⁻¹result- ing from the average of four different n2 values reported in the literature.^18–21

Hence, though the pulse duration used in our CARS experiment is much longer (60 ps) than the one used by Duclèreet al.

(90 fs),¹³ our results prove that a simple spectral filtering of the broadband anti-Stokes wave can remove the vibrational response of the material and successfully extract the real part of the pure electronic response of the third order nonlinear optical susceptibility.

Thus, the experimental data are recorded for high wavenumbers (between 1000 and 3000cm⁻¹), far enough from the vibrational signature.

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B. In-plane modulation of the nonlinear refractive index

Third order nonlinear polarization in a given directionican be written as a function of the incident electric fieldEj,E_kandE_lin the directionsj,kandlaccording to Eq.5.

P⁽³⁾_i =ε0∑

jkl

χ⁽³⁾_ijklEjEkEl (5)

χ_ijkl⁽³⁾ is an element of the χ⁽³⁾_NR tensor which has some angular dependence.

For the same c-cut TeO2 − α single crystal, the (⃗a-TeO2,⃗b- TeO2) in-plane angular dependence of the nonlinearity was recently assessed by Duclèreet al.,¹³via the z-scan technique. While rotating the crystal around the four-fold symmetry c-axis, the in-plane modulation of theχ⁽³⁾was clearly evidenced as depicted inFig. 6b through the amplitude variation of the normalized transmittance ΔTp−v(converted here in values ofn2for the comparison) and, in particular, the values of some elements of theχ⁽³⁾ tensor (namely Re[χ⁽³⁾xxxx]andRe[χxxyy⁽³⁾]) were derived.¹³

Hence, in addition to the relative values of nonlinear refractive index discussed in Sec. III A, it is also expected to access the same angular dependence within the (⃗a-TeO2,⃗b-TeO2) plane, thanks to our CARS setup. We have seen in Eq. 2 that CARS intensity is proportional to the square ofRe[χ_NR⁽³⁾], provided that it is recorded far enough (between 1000 cm⁻¹ and 3000 cm⁻¹) from any vibrational response of the medium. We then recorded in this range the mean evolution of the NRB intensity and plotted its square root for different rotation stage angles from 0^○ to 90^○. SoFig. 6reveals, indeed, that CARS data present such modulation of the nonlinear refractive index n2 with the rotation of the stage (obviously, such modulation is totally absent for both silica and SF57 reference glass samples). The modulation depth reaches ∼15.1%, whereas the one deduced from z-scan experiments was ∼11.5%. Again, results from CARS experiments fall within the same range as those obtained from z-scan experiments.

The differences could be related, of course, to the experimental error but also to the spectral dependence of the nonlinear refractive index as the z-scan experiment was conducted at 800 nm, whereas the current CARS measurement is runned with a pump at 1064 nm.

Further analysis focuses on the angular positions of the maximum and minimum observed inFig. 6. Based on the specific experimental configuration described inFig. 1, where the pump laser is linearly polarized along the y direction, the latter forming a 45^○ angle with the⃗b-TeO2and⃗a-TeO2lattice vectors, and as previously discussed in details by Duclèreet al.,¹³respective positions of the maximum and minimum of the in-plane nonlinear response are theoretically expected along the<110>and<100>directions of the crystal lattice. Additionally, paratellurite material is known for being optically active.^14,23Indeed, the polarization direction of the laser beam can progressively dextro-rotate along the propagation across the thickness of the crystal, and emerge from the latter with a rotation angleρ(given in^○/mm), according to a law modelised by Kolesnikovet al.²³and summarized here with the Eq.6:

ρ⁻¹=a+bλ²ln(λ) (6) whereλis the wavelength (in Angströms) and a and b are two known parameters (a=−0.00310 andb= 4.17× 10⁻¹¹). Thus, for pre- vious z-scan experiments (Fig. 6b), the respective positions for the maximum and minimum intensities are shifted in respect to 0^○and 45^○, because the beam waist crosses the whole sample thickness, and consequently the known optical activity of paratellurite^14,23must be taken into account.¹³Considering the optical activity of such TeO2

−αcrystal, with a thickness ofl= 565μmwhich induces a dextro rotation to⃗Epumpby an angleρ, one expects to detect a minimum of Re[χ⁽³⁾_NR]for an angular position of 45^○+ρl/2, instead of 45^○.¹³The position of the minimum evidenced for the set of z-scan data theoretically falls at∼58.9^○(at 800 nm) and experimentally, the result of the fitting gives a minimum evidenced at∼57.4^○, which is in good agreement with the theory.

In our current CARS configuration, beside a very small beam waist (axial spot size≤2μm) by the use of x60 excitation objective, the focus plane of excitation beams is near the lower physical surface of the crystal. The thickness crossed by beam waist is, thus, very small against the crystal total thickness of 565 μm and the optical activity can be neglected. Hence, the maximum and minimum CARS signals are respectively spotted at∼0^○ and

∼45^○ (Fig. 6a), which is also in good agreement with the theory.

Fig. 6finally attests again the good matching between the two sets of data, and demonstrates the relevance of conducting such CARS experiments in the aim of accessing third-order nonlinear optical properties.

FIG. 6. In-plane angular dependence of the nonlinear refractive indexn₂in CARS experiments (a) in comparison with z-scan data (b).¹³The angular position of the minimum value ofn2is highlighted (black dashed line) in each case (45^○in CARS and 57.4^○in z-scan). Red line: sine fit of experimental data.

AIP Advances9, 105301 (2019); doi: 10.1063/1.5113478 9, 105301-5

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In this study we demonstrated that the real part of the pure electronic response of a paratellurite single crystal TeO2−αcan be obtained by using picosecond M-CARS experiment. By a broadband spectral analysis of the CARS intensity, the electronic contribution can be separated from the vibrational one without using ultrashort pulse duration. The nonresonant background signature of the sample is compared to those obtained with referenced materials such as fused silica and SF57 glasses. Such comparison provides then the quantitative evaluation of the meann2value∼5.72×10⁻¹⁹m²W⁻¹ for TeO2−αcrystal. The obtained value is in excellent agreement with the results recently published by Duclèreet al.¹³by means of z-scan technique in femtosecond regime, and with the THG data from Kimet al.²² collected on pure TeO2 glass. Additionally, we also accessed the in-plane modulation ofn2of TeO2−αcrystal. If M-CARS is commonly used to obtain the vibrational signature of samples, we demonstrated in this work that it can also be efficient to extract the real part of the nonresonant third order susceptibility. Such demonstration opens the way to spatial mapping of complex nonlinear samples including different molecular structures, as ceramics or glass-ceramics.

ACKNOWLEDGMENTS

We wish to acknowledge the support of French defense agency (Direction Générale de l’Armement) and the French national research agency (ANR) through the NEOSPRAM project (ANR- 14-ASTR-0014). This work benefited also of a financial support via the TRAFIC project (ANR-18-CE08-0016-01). Finally Z. Rajaofara wishes to thank the Région Nouvelle-Aquitaine for partial funding of his PhD, within the frame of the NEMATUUM project.

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